DOCSLIB.ORG

Determination of the Neutron Magnetic Moment

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Determination of the Neutron Magnetic Moment DETERMINATION OF THE NEUTRON MAGNETIC MOMENT G.L. Greene and N.F. Ramsey Harvard University, Cambridge, Massachusetts 02138 W. Mampe Institut Laue-Langevin, 380A2 Grenoble, France -^... J.M. Pendlebury and K. Smith \ '"-> -*, University of Sussex, Falmer, Brighton, BNI 9 QH, United Kingdom V!.B. Dress and P.D. Miller Oak Ridge National Laboratory, Oak Ridge, Tennessee 37838 Paul Perrin Centre d'Etudes Nucleaires, 38042 Grenoble, France The neutron magnetic inomenL has bae» measured with an improvement of a factor of 100 over the previous best neasurement. Using a magnetic resonance spectrometer of the separated oscillatory field type capable of determining a resonance signal for both neutrons and protons (in flowing 1^0), we find u /v = 0.68497935(17) (0.25 ppm). The neutron magnetic moment: can also be n p expressed without loss of accuracy in a variety of other units. Key words: Flowing water NMR; magnetic resonance; neutron magnetic moment; particle properties. Current address: Gibbs Laboratory, Physics Department, Yale University, New Haven, Conn. 06520 ^^ ^ ^ .^^ ^ MASTER 1. Introduction The realization that the neutron, a neutral particle, possesses a non-zero magnetic moment has been of considerable importance in the development of nuclear and particle physics. Even before any explicit measurement of p had been made, there was a strong indication that u f 0 from comparisons of the proton and deuteron magnetic moments u and p . If the neutron and proton combine in a pure S. state to form the deuteron, one would expect p_ = p + p . Early measurements of p and pD gave, according to this relation, p = -1.8 p., where p., is the nuclear magneton, n N N According to Dirac Theory, which assumes structureless, spin 1/2 particles, p =0 and p = p,,. The anomolous moments are defined as the n p h differences between the actual moments and the Dirac moments. The first serious attempt to explain the anomolous moments of the nucleons was made by Frolich, Heitler and Kemmer [1] in 1938. Their "meson exchange theory" pre- dicted equal magnitudes and opposite signs for the anomolous proton and neutron moments [2], The actual magnitudes of the moments are much more difficult to obtain using this theory. Though subsequently refined by many others [3J the initial conclusions of Frolich, Heitler and Ketr.mer adequately summar- ized the state of the theoretical understanding of the neutron magnetic moment until the introduction of the quark, model. The first explicit measurement of Lhe neutron magnetic moment was made by Alverez and Bloch [4] in 19'iO. Using Rabi's magnetic resonance technique with a neutron beam obtained by deuteron bombardment of Be, they obtained a value of |u | = 1.93 ± 0.02 p . In general, no information about the sign of a magnetic moment is obtainable from a resonance experiment utilizing a purely oscillating magnetic field (In 1949 Rogers and Staub [5] determined the sign of p using a resonance technique that employed a rotating field. As had been thought, the sign was negative.) 2 The discovery by Kellog, Rabi, Ramsey and Zacharias [6] that the deuteron has an electric quadropole moment implied that the ground state of the 3 deuteron could not, in fact, be accurately described by a pure S1 state but must have some admixture of D state. Thus the additivity of neutron and proton moments in the deuteron could not be exact. It was therefore of great interest to determine p more accurately so that it could be compared with the well known values of u and p_. P D In 1947 Arnold and Roberts [7], using a neutron beam from a reactor, determined p in a resonance experiment with a single oscillatory field. They were able to obtain a more accurate value of |u | = 1.9103(12) u^ by using the then novel technique of NMR as a means of field calibration. About the same time, Bloch, Micodemus and Staub [81 also obtained a more accurate value for p . They reported their result as the ratio of neutron to proton moment |p /p | = 0.685001(30). With these more accurate values for u , it was possible to determine the D.. admixture in the deuteron ground state by two independent means, through the deuteron electric quadropole moment, or by comparison between u , u and Pn- Gratifyingly, these independent values were consistant. With the introduction of the quark model an appealing explanation for the value of the ratio of the neutron moment to the proton moment emerged. Sakita [9] and Beg, Lee and Pais [10] pointed out that this ratio should be p /p = -2/3 [11] if the internal symmetry SU(3) is bioken only by electro- sagnetism. In this model, the ratios of ?11 the baryon ifioments are uniquely determined and easily calculated (Their absolute magnitudes are dependent on the quark magnetic moments. Determining these would require knowledge of the quark masses). The agreement between theory and experiment for u /u is considerably better than for other baryon pairs and is striking for such a simple theory. The approximately 3% discrepancy between theory and experiment should not be viewed as a significant disagreement. SU(3)® SU(2) (i.e 3 similar quarks with spin 1/2) is known to be an incomplete description for strongly interacting particles. At the initiation of the vork reported here, the uncertainty associated with theory far exceeded the experimental error of the best measurement of y [12]. As a result, theoretical considerations did not provide the dominant n motivation for the current work. Rather, the possibility of a substantial improvement in our knowledge of a fundamental particle property as well as the opportunity to demonstrate an elegant, new experimental technique prompted our effort. The most accurate determination of u , prior to the work reported here, was that of Corngold, Cohen and Ramsey [12]. This experiment involved a thermal neutron beam and benefited from the use of the separated oscillatory field method. A result of |p /p | = 0.685039(17) was obtained. The major limitation to the accuracy of this measurement arose from the method used to calibrate the magnetic field. An NMR probe of small dimensions was employed to determine the field at a number of discrete locations. This field map was then used to give the appropriate field average by a pointwise integration. The discrete nature of this stepwise integration led to the dominant error in the experimental result. The current work benefit ted from several advances in experimental technique. Access to the high flux reactor of the Institut Laue-Langevin at Grenoble, France, allowed the use of an intense "cold" neutron beam. Such "cold" beams are characterized by low beam velocities. This led to an improvement of a factor of -5 over the line width obtained by Cohen, Corngold and Ramsey [12]. An additional advantage to the use of "cold" neutrons lies in the ability to employ neutron guides to reduce beam divergence and thei.^ ore increase the flux. Such guides also allowed a novel field calibration technique which provided the major improvement in experimental sensitivity. Following a suggestion of Purcell {13] made some time ago, the field was monitored by obtaining a separated oscillatory field resonance signal with water flowing through the neutron guide. In this fashion, the field average taken by the protons in the water is the same as that taken by the neutrons. Since all the relevant diamagnetic corrections for protons in water are known to high accuracy, a direct measurement of the ratio of the neutron magnetic moment to the proton magnetic moment was obtained. From this result, the magnetic moment of the neutron can be expressed in a variety of other units. 2. Apparatus The aim of the experimental technique was to measure the Larmor precession frequency for neutrons and protons (in water) in precisely the same volume as nearly simultaneously as possible. With the use of a neutron guide (a glass tube of circular cross-section) it was a straight forward matter to confine neutrons and water in the sair.e volume. One simply let the water flow through the neutron guide. This procedure,however precluded the possibility of determining the resonance frequency for neutrons and protons with exact simultaneity. To insure that no spurious effects resulted from drifts during the time required to make a change-over from neutron beam to flowing water, a second, parallel tube was installed in the spectrometer. Water was continuously sent through this tube to provide a field monitor. By alternating neutrons and protons in the principal tube t:hile protons flowed continuously in the monitor tube, errors due to field drifts could be detected and reduced to an insignificant level. This technique has been discussed in detail elsewhere The cold source at the high flux reactor of the Institut Laue-Langevin in Grenoble provided the source of neutrons used in this experiment. The flux through the apparatus was typically 1.5 x 10 neutrons/s. The neutrons were polarized by glancing reflection from a magnetized mirror. A similar mirror was used to analyze the neutron polarization at the exit of the spec- trometer. The neutrons were detected by a Li loaded glass scintillator coupled to a photo-multiplier. The protons in the flowing water were polarized by passage through a chamber placed in a high (~2kG) pre-polarizing magnet. As the protons spent more than one longitudinal relaxation time in this field, their polarization could be approximated by a simple Boltzman distribution. While the degree of polarization so obtained was very small, the enormous flux (by molecular beam standards) led to an easily detected signal. The proton polarization at exit was detected in a second high field region (-4kG) with slightly modified commercial NMR equipment.
Load more

Recommended publications
  • Experiment QM2: NMR Measurement of Nuclear Magnetic Moments
    Physics 440 Spring (3) 2018 Experiment QM2: NMR Measurement of Nuclear Magnetic Moments Theoretical Background: Elementary particles are characterized by a set of properties including mass m, electric charge q, and magnetic moment µ. These same properties are also used to characterize bound collections of elementary particles such as the proton and neutron (which are built from quarks) and atomic nuclei (which are built from protons and neutrons). A particle's magnetic moment can be written in terms of spin as µ = g (q/2m) S where g is the "g-factor" for the particle and S is the particle spin. [Note 2 that for a classical rotating ball of charge S = (2mR /5) ω and g = 1]. For a nucleus, it is conventional to express the magnetic moment as µ A = gA µN IA /! where IA is the "spin", gA is the nuclear g-factor of nucleus A, and the constant µN = e!/2mp (where mp= proton mass) is known as the nuclear magneton. In a magnetic field (oriented in the z-direction) a spin-I nucleus can take on 2I+1 orientations with Iz = mI! where –I ≤ mI ≤ I. Such a nucleus experiences an orientation- dependent interaction energy of VB = –µ A•B = –(gA µN mI)Bz. Note that for a nucleus with positive g- factor the low energy state is the one in which the spin is aligned parallel to the magnetic field. For a spin-1/2 nucleus there are two allowed spin orientations, denoted spin-up and spin-down, and the up down energy difference between these states is simply given by |ΔVB| = VB −VB = 2µABz.
    [Show full text]
  • Lecture #4, Matter/Energy Interactions, Emissions Spectra, Quantum Numbers
    Welcome to 3.091 Lecture 4 September 16, 2009 Matter/Energy Interactions: Atomic Spectra 3.091 Periodic Table Quiz 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 Name Grade /10 Image by MIT OpenCourseWare. Rutherford-Geiger-Marsden experiment Image by MIT OpenCourseWare. Bohr Postulates for the Hydrogen Atom 1. Rutherford atom is correct 2. Classical EM theory not applicable to orbiting e- 3. Newtonian mechanics applicable to orbiting e- 4. Eelectron = Ekinetic + Epotential 5. e- energy quantized through its angular momentum: L = mvr = nh/2π, n = 1, 2, 3,… 6. Planck-Einstein relation applies to e- transitions: ΔE = Ef - Ei = hν = hc/λ c = νλ _ _ 24 1 18 Bohr magneton µΒ = eh/2me 9.274 015 4(31) X 10 J T 0.34 _ _ 27 1 19 Nuclear magneton µΝ = eh/2mp 5.050 786 6(17) X 10 J T 0.34 _ 2 3 20 Fine structure constant α = µ0ce /2h 7.297 353 08(33) X 10 0.045 21 Inverse fine structure constant 1/α 137.035 989 5(61) 0.045 _ 2 1 22 Rydberg constant R¥ = mecα /2h 10 973 731.534(13) m 0.0012 23 Rydberg constant in eV R¥ hc/{e} 13.605 698 1(40) eV 0.30 _ 10 24 Bohr radius a0 = a/4πR¥ 0.529 177 249(24) X 10 m 0.045 _ _ 4 2 1 25 Quantum of circulation h/2me 3.636 948 07(33) X 10 m s 0.089 _ 11 1 26 Electron specific charge -e/me -1.758 819 62(53) X 10 C kg 0.30 _ 12 27 Electron Compton wavelength λC = h/mec 2.426 310 58(22) X 10 m 0.089 _ 2 15 28 Electron classical radius re = α a0 2.817 940 92(38) X 10 m 0.13 _ _ 26 1 29 Electron magnetic moment` µe 928.477 01(31) X 10 J T 0.34 _ _ 3 30 Electron mag.
    [Show full text]
  • The G Factor of Proton
    The g factor of proton Savely G. Karshenboim a,b and Vladimir G. Ivanov c,a aD. I. Mendeleev Institute for Metrology (VNIIM), St. Petersburg 198005, Russia bMax-Planck-Institut f¨ur Quantenoptik, 85748 Garching, Germany cPulkovo Observatory, 196140, St. Petersburg, Russia Abstract We consider higher order corrections to the g factor of a bound proton in hydrogen atom and their consequences for a magnetic moment of free and bound proton and deuteron as well as some other objects. Key words: Nuclear magnetic moments, Quantum electrodynamics, g factor, Two-body atoms PACS: 12.20.Ds, 14.20.Dh, 31.30.Jv, 32.10.Dk Investigation of electromagnetic properties of particles and nuclei provides important information on fundamental constants. In addition, one can also learn about interactions of bound particles within atoms and interactions of atomic (molecular) composites with the media where the atom (molecule) is located. Since the magnetic interaction is weak, it can be used as a probe to arXiv:hep-ph/0306015v1 2 Jun 2003 learn about atomic and molecular composites without destroying the atom or molecule. In particular, an important quantity to study is a magnetic moment for either a bare nucleus or a nucleus surrounded by electrons. The Hamiltonian for the interaction of a magnetic moment µ with a homoge- neous magnetic field B has a well known form Hmagn = −µ · B , (1) which corresponds to a spin precession frequency µ hν = B , (2) spin I Email address: [email protected] (Savely G. Karshenboim). Preprint submitted to Elsevier Science 1 February 2008 where I is the related spin equal to either 1/2 or 1 for particles and nuclei under consideration in this paper.
    [Show full text]
  • Deuterium Magnetic Resonance: Theory and Application to Lipid Membranes
    Quarterly Reviews of Biophysics 10, 3 (1977), pp. 353-418. Printed in Great Britain Deuterium magnetic resonance: theory and application to lipid membranes JOACHIM SEELIG Department of Biophysical Chemistry, Biocenter of the University of Basel, Klingelbergstrasse 70, C//-4056 Basel, Switzerland I. INTRODUCTION 345 II. THEORY OF DEUTERIUM MAGNETIC RESONANCE 358 A. Deuterium magnetic resonance in the absence of molecular motion 358 1. General theory 358 2. Rotation of the coordinate system 359 3. Principal coordinate system 360 4. Energy levels 362 5. Lineshapes of polycrystalline samples 364 B. Deuterium magnetic resonance of liquid crystals 369 1. Anisotropic motions in liquid crystals 369 2. Deuterium-order parameters in planar-oriented liquid crystals 373 3. Lineshapes for random and cylindrical distributions of liquid crystalline microdomains 377 4. Anisotropic rotation of CD2 and CD3 groups 383 5. Deuterium quadrupole relaxation in anisotropic media 386 III. APPLICATION OF DEUTERIUM MAGNETIC RESONANCE TO LIPID MEMBRANES 388 A. Lipid bilayers composed of soap molecules 388 B. Phospholipid bilayers 393 1. Hydrocarbon region 394 2. Structure and flexibility of the polar head groups 405 REFERENCES 411 23-2 Downloaded from https://www.cambridge.org/core. WWZ Bibliothek, on 14 Nov 2017 at 10:27:10, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0033583500002948 354 J- SEELIG I. INTRODUCTION Proton and carbon-13 nmr spectra of unsonicated lipid bilayers and biological membranes are generally dominated by strong proton-proton and proton-carbon dipolar interactions. As a result the spectra contain a large number of overlapping resonances and are rather difficult to analyse.
    [Show full text]
  • 1. Physical Constants 101
    1. Physical constants 101 1. PHYSICAL CONSTANTS Table 1.1. Reviewed 2010 by P.J. Mohr (NIST). Mainly from the “CODATA Recommended Values of the Fundamental Physical Constants: 2006” by P.J. Mohr, B.N. Taylor, and D.B. Newell in Rev. Mod. Phys. 80 (2008) 633. The last group of constants (beginning with the Fermi coupling constant) comes from the Particle Data Group. The figures in parentheses after the values give the 1-standard-deviation uncertainties in the last digits; the corresponding fractional uncertainties in parts per 109 (ppb) are given in the last column. This set of constants (aside from the last group) is recommended for international use by CODATA (the Committee on Data for Science and Technology). The full 2006 CODATA set of constants may be found at http://physics.nist.gov/constants. See also P.J. Mohr and D.B. Newell, “Resource Letter FC-1: The Physics of Fundamental Constants,” Am. J. Phys, 78 (2010) 338. Quantity Symbol, equation Value Uncertainty (ppb) speed of light in vacuum c 299 792 458 m s−1 exact∗ Planck constant h 6.626 068 96(33)×10−34 Js 50 Planck constant, reduced ≡ h/2π 1.054 571 628(53)×10−34 Js 50 = 6.582 118 99(16)×10−22 MeV s 25 electron charge magnitude e 1.602 176 487(40)×10−19 C = 4.803 204 27(12)×10−10 esu 25, 25 conversion constant c 197.326 9631(49) MeV fm 25 conversion constant (c)2 0.389 379 304(19) GeV2 mbarn 50 2 −31 electron mass me 0.510 998 910(13) MeV/c = 9.109 382 15(45)×10 kg 25, 50 2 −27 proton mass mp 938.272 013(23) MeV/c = 1.672 621 637(83)×10 kg 25, 50 = 1.007 276 466 77(10) u = 1836.152 672 47(80) me 0.10, 0.43 2 deuteron mass md 1875.612 793(47) MeV/c 25 12 2 −27 unified atomic mass unit (u) (mass C atom)/12 = (1 g)/(NA mol) 931.494 028(23) MeV/c = 1.660 538 782(83)×10 kg 25, 50 2 −12 −1 permittivity of free space 0 =1/μ0c 8.854 187 817 ..
    [Show full text]
  • CODATA RECOMMENDED VALUES of the FUNDAMENTAL PHYSICAL CONSTANTS: 2014 NIST SP 961 (Sept/2015) Values From: P
    CODATA RECOMMENDED VALUES OF THE FUNDAMENTAL PHYSICAL CONSTANTS: 2014 NIST SP 961 (Sept/2015) Values from: P. J. Mohr, D. B. Newell, and B. N. Taylor, arXiv:1507.07956 Amoreextensivelistingofconstantsisavailableintheabove reference and on the NIST Physics Laboratory Web site physics.nist.gov/constants. The number in parentheses is the one-standard-deviation uncertainty in the last two digits of the given value. Quantity Symbol Numerical value Unit Quantity Symbol Numerical value Unit −1 speed of light in vacuum c, c0 299 792 458 (exact) m s muon g-factor −2(1 + aµ) gµ −2.002 331 8418(13) −7 −2 magnetic constant µ0 4π × 10 (exact) N A muon-proton magnetic moment ratio µµ/µp −3.183 345 142(71) −7 −2 −27 =12.566 370 614... × 10 NA proton mass mp 1.672 621 898(21) × 10 kg 2 −12 −1 electric constant 1/µ0c ϵ0 8.854 187 817... × 10 Fm in u 1.007 276 466 879(91) u −11 3 −1 −2 2 Newtonian constant of gravitation G 6.674 08(31) × 10 m kg s energy equivalent in MeV mpc 938.272 0813(58) MeV −34 Planck constant h 6.626 070 040(81) × 10 Js proton-electron mass ratio mp/me 1836.152 673 89(17) −15 −26 −1 in eV s 4.135 667 662(25) × 10 eV s proton magnetic moment µp 1.410 606 7873(97) × 10 JT −34 h/2π h¯ 1.054 571 800(13) × 10 Js to nuclear magneton ratio µp/µN 2.792 847 3508(85) −16 ′ ′ −6 in eV s 6.582 119 514(40) × 10 eV s proton magnetic shielding correction 1 − µp/µp σp 25.691(11) × 10 −19 ◦ elementary charge e 1.602 176 6208(98) × 10 C (H2O, sphere, 25 C) −15 8 −1 −1 magnetic flux quantum h/2e Φ0 2.067 833 831(13) × 10 Wb proton gyromagnetic ratio
    [Show full text]
  • A Quantitative Determination of the Neutron Moment in Absolute Nuclear Magnetons
    Luis W. Alvarez Phys. Rev. 57, 111 1940 A Quantitative Determination of the Neutron Moment in Absolute Nuclear Magnetons LUIS W. ALVAREZ, Radiation Laboratory, Department of Physics, University of California, Berkeley, California and F. BLOCH, Department of Physics, Stanford University, Polo Alto, California (Received October 30, 1939) Abstract The magnetic resonance method of determining nuclear magnetic moments in molecular beams, recently described by Rabi and his col- laborators, has been extended to allow the determination of the neu- tron moment. In place of deflection by inhomogeneous magnetic fields, magnetic scattering ie used to produce and analyze the polarized beam of neutrons. Partial depolarization of the neutron beam is observed when the Larmor precessional frequency of the neutrons in a strong field is in resonance with a weak oscillating magnetic field normal to the strong field. A knowledge of the frequency and field when the res- onance is observed, plus the assumption that the neutron spin is 1/2 yields the moment directly. The theory of the experiment is developed in some detail, and a description of the apparatus is given. A new method of evaluating magnetic moments in all experiments using the resonance method is described. It is shown that the magnetic moment of any nucleus may be determined directly in absolute nuclear mag- netons merely by a measurement of the ratio of two magnetic fields. These two fields are (a) that at which resonance occurs in a Rabi type experiment for a certain frequency, and (b) that at which protons are accelerated in a cyclotron operated on the nth harmonic of that fre- quency.
    [Show full text]
  • A Parts-Per-Billion Measurement of the Antiproton Magnetic Moment C
    OPEN LETTER doi:10.1038/nature24048 A parts-per-billion measurement of the antiproton magnetic moment C. Smorra1,2, S. Sellner1, M. J. Borchert1,3, J. A. Harrington4, T. Higuchi1,5, H. Nagahama1, T. Tanaka1,5, A. Mooser1, G. Schneider1,6, M. Bohman1,4, K. Blaum4, Y. Matsuda5, C. Ospelkaus3,7, W. Quint8, J. Walz6,9, Y. Yamazaki1 & S. Ulmer1 Precise comparisons of the fundamental properties of matter– of 5.3 MeV. These particles can be captured and cooled in Penning traps antimatter conjugates provide sensitive tests of charge–parity–time by using degrader foils, a well timed high-voltage pulse and electron (CPT) invariance1, which is an important symmetry that rests on cooling17. The core of our experiment is formed by two central devices; basic assumptions of the standard model of particle physics. a superconducting magnet operating at a magnetic field of B0 =​ 1.945 T, Experiments on mesons2, leptons3,4 and baryons5,6 have compared and an assembly of cylindrical Penning-trap electrodes18 (partly shown different properties of matter–antimatter conjugates with fractional in Fig. 1b) that is mounted inside the horizontal bore of the magnet. uncertainties at the parts-per-billion level or better. One specific A part of the electrode assembly forms a spin-state analysis trap with 2 quantity, however, has so far only been known to a fractional an inhomogeneous magnetic field Bz,AT(z) = B0,AT + B2,ATz , 7,8 −2 uncertainty at the parts-per-million level : the magnetic moment at B0,AT =​ 1.23 T and B2,AT =​ 272(12) kT m , and a precision trap 5 of the antiproton, μ p.
    [Show full text]
  • Chapter 1 MAGNETIC NEUTRON SCATTERING
    Chapter 1 MAGNETIC NEUTRON SCATTERING. And Recent Developments in the Triple Axis Spectroscopy Igor A . Zaliznyak'" and Seung-Hun Lee(2) (')Department of Physics. Brookhaven National Laboratory. Upton. New York 11973-5000 (')National Institute of Standards and Technology. Gaithersburg. Maryland 20899 1. Introduction..................................................................................... 2 2 . Neutron interaction with matter and scattering cross-section ......... 6 2.1 Basic scattering theory and differential cross-section................. 7 2.2 Neutron interactions and scattering lengths ................................ 9 2.2.1 Nuclear scattering length .................................................. 10 2.2.2 Magnetic scattering length ................................................ 11 2.3 Factorization of the magnetic scattering length and the magnetic form factors ............................................................................................... 16 2.3.1 Magnetic form factors for Hund's ions: vector formalism19 2.3.2 Evaluating the form factors and dipole approximation..... 22 2.3.3 One-electron spin form factor beyond dipole approximation; anisotropic form factors for 3d electrons..................... 27 3 . Magnetic scattering by a crystal ................................................... 31 3.1 Elastic and quasi-elastic magnetic scattering............................ 34 3.2 Dynamical correlation function and dynamical magnetic susceptibility ............................................................................................
    [Show full text]
  • Neutrons and Magnetism
    Collection SFN 13, 01002 (2014) DOI: 10.1051/sfn/20141301002 C Owned by the authors, published by EDP Sciences, 2014 Neutrons and magnetism Mechthild Enderle Institut Laue-Langevin, 6, Rue Jules Horowitz, BP. 156, 38042 Grenoble Cedex, France Abstract. Neutron scattering is a unique technique in magnetism, since it measures directly the Fourier transform of the time-dependent magnetic pair correlations. The neutron interacts only weakly with matter, so that each neutron normally only scatters once in the sample volume. The dynamic pair correlation functions are thus probed in the whole volume of the sample. Here we summarize the relevant formalism and approximations for neutron scattering on magnetic materials, focusing on the investigation of single crystals. The lecture aims to stimulate – not to replace – the study of the relevant literature [1–9]. 1. THERMAL NEUTRON SCATTERING 1.1 Properties of the neutron We recall some important properties of the neutron: – wave (interference, even with itself) – particle (mass m, energy-momentum relation, interactions) – lifetime of free neutron: 15 min (allows to do experiments) p = k = 2 – momentum = p2 = 2 2 = 2 2 – energy E 2m 2m k 2.072 k meV Å – no charge e – spin 1/2 and magnetic moment n =−N ˆ, where = 1.913, N = is the nuclear magneton, 2mp and ˆ is the Pauli spin operator. 1.2 Master equation All interactions of thermal (slow) neutrons with matter are weak, either due to the weakness of the interaction itself (interaction with the unpaired electrons, Foldy, spin-orbit), or, as in the case of the strong interaction with the nucleus, due to the extreme short-range character of the interaction and the extreme “dilution” of the point-like scattering nuclei in the scattering volume.
    [Show full text]
  • I Magnetism in Nature
    We begin by answering the first question: the I magnetic moment creates magnetic field lines (to which B is parallel) which resemble in shape of an Magnetism in apple’s core: Nature Lecture notes by Assaf Tal 1. Basic Spin Physics 1.1 Magnetism Before talking about magnetic resonance, we need to recount a few basic facts about magnetism. Mathematically, if we have a point magnetic Electromagnetism (EM) is the field of study moment m at the origin, and if r is a vector that deals with magnetic (B) and electric (E) fields, pointing from the origin to the point of and their interactions with matter. The basic entity observation, then: that creates electric fields is the electric charge. For example, the electron has a charge, q, and it creates 0 3m rˆ rˆ m q 1 B r 3 an electric field about it, E 2 rˆ , where r 40 r 4 r is a vector extending from the electron to the point of observation. The electric field, in turn, can act The magnitude of the generated magnetic field B on another electron or charged particle by applying is proportional to the size of the magnetic charge. a force F=qE. The direction of the magnetic moment determines the direction of the field lines. For example, if we tilt the moment, we tilt the lines with it: E E q q F Left: a (stationary) electric charge q will create a radial electric field about it. Right: a charge q in a constant electric field will experience a force F=qE.
    [Show full text]
  • Dias Nummer 1
    Madan Mohan Malaviya Univ. of Technology, Gorakhpur MPM: 203 NUCLEAR AND PARTICLE PHYSICS UNIT –I: Nuclei And Its Properties Lecture-5 By Prof. B. K. Pandey, Dept. of Physics and Material Science 24-10-2020 Side 1 Madan Mohan Malaviya Univ. of Technology, Gorakhpur Nuclear Magnetic Moment • The Magnetic dipole moment produced by a current loop is given as 훍 = iA Where I is the current and A is the area of the loop • A spinless particle having charge e revolving in a loop will set a magnetic dipole moment. If particle revolves with velocity v in a circular orbit of radius r, then equivalent current • i= 퐶ℎ푎푟푒 = 푒 = 푒 = 푒푣 푡푚푒 푝푒푟표푑 푇 2휋푟/푣 2휋푟 푒푣 푒푣푟 • Magnetic dipole moment = 훍 = iA= 휋푟2, i.e. 훍 = 푙 2휋푟 푙 2 • The orbital angular momentum of the particle L= mvr • The ratio of magnetic dipole moment to the orbital angular momentum is called the gyro-magnetic ratio i.e. 휇 푒푣푟/2 푒 • 훾 = 푙 = = 퐿 푚푣푟 2푚 24-10-2020 Side 2 Madan Mohan Malaviya Univ. of Technology, Gorakhpur Nuclear Magnetic Moment Contd.. Ԧ • The relation will also hold for the components of two vectors 휇푙 and 푙 along any direction ( in the direction of magnetic field) • Z- component of dipole magnetic moment 푒 푒 • (휇 ) = 퐿 = 푚 ћ 퐿 푍 2푚 푍 2푚 푙 푒ћ • (휇 ) = 푚 퐿 푍 2푚 푙 • This is the relation for the magnetic dipole moment along the direction of magnetic field due to the orbital motion of electron in an atom. • By analogy same orbital motion may hold for proton inside the nucleus.
    [Show full text]